Getting Around the Loop. From How Far Above the Ground Does the Roller Coaster Need to Start? (page 2)
With a low-friction sliding object car, such as a cart with wheels or a roller coaster car, the height must be at least 2.5 times the radius of the loop. Actual loops require slightly greater height to overcome friction.
For rolling objects, such as a steel ball or marble, some of the potential energy is tied up in rolling, so the height must be at least 2.7 times the radius of the loop (again, without accounting for frictional losses).
Why It Works
The potential energy you start with (by raising it to certain height on the track) is changed into kinetic energy. The higher your release point, the faster it goes. If the object is rolling rather than sliding, some of the potential energy is used to get the object rolling. If there is friction along the way, some additional potential energy is consumed.
To negotiate the loop, the centripetal force (provided by the track to maintain a circular path) must just equal the force of gravity. With less velocity, it will fall before completing the loop. With extra velocity, it will get through with some energy to spare.
Other Things to Try
Now that you have one loop down, you can try a similar track with more than one loop. You still only need one ramp to give the marble an initial velocity.
Total mechanical energy is conserved. Potential energy is converted to kinetic energy and vice versa.
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